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Day 104: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Matrices. This type asked 2 times: 2021 Paper 3, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 2 of this type

    74
    Let A=[02−3−2013−10]A = \begin{bmatrix} 0 & 2 & - 3 \\ - 2 & 0 & 1 \\ 3 & - 1 & 0 \end{bmatrix} and B be a matrix such that B(I−A)=I+AB(I - A) = I + A. Then the sum of the diagonal elements of BTBB^{T}B is equal to

  2. Question 2

    Permutations and Combinations. This type asked 2 times: 26 Jul 2022, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 2 of this type

    75
    Let S denote the set of 4-digit numbers abcd such that a>b>c>da > b > c > d and P denote the set of 5-digit numbers having product of its digits equal to 20. Then n(S)+n(P)n(S) + n(P) is equal to........... .

  3. Question 3

    Conic Sections. This type asked 2 times: 29 Jun 2022, 23 Jan 2026 S1. This one: 23 Jan 2026 S1 See all 2 of this type

    51
    Let the domain of the function f(x)=log⁡3log⁡5log⁡7(9x−x2−13)f(x) =\log_{3}\log_{5}\log_{7}\left( 9x -x^{2}- 13 \right) be the interval (m,n)(m,n). Let the hyperbola x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 have eccentricity n3\frac{n}{3} and the length of the latus rectum 8m3\frac{8m}{3}. Then b2−a2b^{2}-a^{2} is equal to :

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  4. Question 4

    Conic Sections. This type asked 2 times: 30 Jan 2024, 22 Jan 2026 S2. This one: 22 Jan 2026 S2 See all 2 of this type

    61
    Let P(10,215)P(10,2\sqrt{15}) be a point on the hyperbola x2a2−y2 b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{{\text{ }b}^{2}}= 1, whose foci are S and S′S^{'}. If the length of its latus rectum is 8 , then the square of the area of △PSS′\bigtriangleup PSS^{'} is equal to :

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  5. Question 5

    Binomial Theorem. This type asked 2 times: 6 Apr 2024, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 2 of this type

    66
    The coefficient of x48x^{48} in (1+x)+2(1+x)2+3(1+x)3+….+100(1+x)100(1 + x) + 2(1 + x)^{2}+ 3(1 + x)^{3}+ \ldots. + 100(1 + x)^{100} is equal to :

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